Is the correct answer listed? (prob. spinner lands on even number, or on number < 4)

MIIF

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Is the correct answer listed? (prob. spinner lands on even number, or on number < 4)

IMG_20180329_121716.png


I tried to answer it and got 3/4 or 6/8 after using the union set operation for 4/8 or 1/2 and 3/8, based on what is being asked in the problem.
 
IMG_20180329_121716.png


I tried to answer it and got 3/4 or 6/8 after using the union set operation for 4/8 or 1/2 and 3/8, based on what is being asked in the problem.
By what reasoning did you arrive at your answer? You noted first that there are eight numbers on the spinner board. You listed out the numbers that are less than 4, but are not even (assuming the "or" here is the "exclusive or", or XOR, meaning "one of these conditions, but not both"). You listed out the numbers that are even, but are not less than 4. From ONE of the lists, you crossed out any duplicates, so you're not counting anything twice. You counted the remaining numbers and... got what? ;)
 
By what reasoning did you arrive at your answer? You noted first that there are eight numbers on the spinner board. You listed out the numbers that are less than 4, but are not even (assuming the "or" here is the "exclusive or", or XOR, meaning "one of these conditions, but not both"). You listed out the numbers that are even, but are not less than 4. From ONE of the lists, you crossed out any duplicates, so you're not counting anything twice. You counted the remaining numbers and... got what? ;)
What do you mean? I arrived at my answer on the basis that the statement is pertaining to the "or" that implies the union set operation, which is supported by this website: https://www.mathplanet.com/education/pre-algebra/probability-and-statistic/probability-of-events.

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What do you mean?
What do I mean by... what?

I arrived at my answer on the basis that the statement is pertaining to the "or" that implies the union set operation, which is supported by this website: https://www.mathplanet.com/education/pre-algebra/probability-and-statistic/probability-of-events.
Okay. But, as you noted, your answer is not among the answer-options listed. If one uses the exclusive, rather than the inclusive, "or", then one can arrive at one of the answer options.

So either the exercise answer-options are wrong, or the use of the inclusive "or" is wrong. Consult your instructor for specifics. ;)
 
IMG_20180329_121716.png


I tried to answer it and got 3/4 or 6/8 after using the union set operation for 4/8 or 1/2 and 3/8, based on what is being asked in the problem.
How many of these eight numbers are even OR less than 4.
Is 1 even or less than 4?
Is 2 even or less than 4?
Is 3 even or less than 4?
Is 4 even or less than 4?
Is 5 even or less than 4?
Is 6 even or less than 4?
Is 7 even or less than 4?
Is 8 even or less than 4?

Count the number of times you said yes and divide that number by 8. Reduce if necessary. Done
 
How many of these eight numbers are even OR less than 4.
Is 1 even or less than 4?
Is 2 even or less than 4?
Is 3 even or less than 4?
Is 4 even or less than 4?
Is 5 even or less than 4?
Is 6 even or less than 4?
Is 7 even or less than 4?
Is 8 even or less than 4?

Count the number of times you said yes and divide that number by 8. Reduce if necessary. Done

MIIF did just that, and got the correct answer. The issue is that 3/4 is not one of the choices. So the problem itself is bad.

You can also do it this way:

P(even OR <4) = P(even) + P(<4) - P(even AND <4) = 4/8 + 3/8 - 1/8 = 6/8 = 3/4
 
How many of these eight numbers are even OR less than 4.
Is 1 even or less than 4?
Is 2 even or less than 4?
Is 3 even or less than 4?
Is 4 even or less than 4?
Is 5 even or less than 4?
Is 6 even or less than 4?
Is 7 even or less than 4?
Is 8 even or less than 4?

Count the number of times you said yes and divide that number by 8. Reduce if necessary. Done
So, it's still 6/8 or 3/4 since reduction isn't necessary.

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MIIF did just that, and got the correct answer. The issue is that 3/4 is not one of the choices. So the problem itself is bad.

You can also do it this way:

P(even OR <4) = P(even) + P(<4) - P(even AND <4) = 4/8 + 3/8 - 1/8 = 6/8 = 3/4
MIIF listed four distinct answers so I was not sure that the OP was completely confident in their original answer. Yes, I saw that the answer was not listed.
 
?.

What do I mean by... what?
What did you mean regarding the answer that uses the exclusive "or"? I just came across this problem while reading the softcopy of a learning material, which does not directly contain a connection with the exclusive "or" and inclusive "or." ("Not directly" because, based from what I've read online, the inclusive "or" may correspond to the use of the union set operation, which is present in the material, and the exclusive "or" really has no tie to the material)
Okay. But, as you noted, your answer is not among the answer-options listed. If one uses the exclusive, rather than the inclusive, "or", then one can arrive at one of the answer options.

So either the exercise answer-options are wrong, or the use of the inclusive "or" is wrong. Consult your instructor for specifics. ;)
As I have said before, the exclusive "or" is nowhere to be found in the material, and this is actually the first time I've encountered it, along with the inclusive "or, " which is, based from my research, really just the union set operation in this case. Here is what I mean:
IMG_20180330_081406.jpg
IMG_20180330_081628.jpg
IMG_20180330_081730.jpg
So, the first image was taken from my learning material, which only mentions the quality of being "exclusive" as the quality of being "mutually exclusive" of 2 events in an experiment. This definition is extended with the help of the second picture. As for the last picture, it shows the difference between the exclusive "or" and inclusive "or" that you're talking about, and, based from my understanding and research, the exclusive "or," in this case, would just amount to 2 possible correct answers among the choices (B. and C.).

I really don't see the visible connection between the material and the exclusive "or," and, by the way, I don't have an instructor for this as I am just doing an advance reading on the material since it's summer break for me. (Oh, and since I just got the material online and not from someone I personally know or my school, I could provide the link/attachment if needed.)
 
MIIF listed four distinct answers so I was not sure that the OP was completely confident in their original answer. Yes, I saw that the answer was not listed.

Actually, I think there's only one answer in their post, although it was written quite poorly, and, frankly, it was kind of a mess. Here's what I interpreted it as saying:

I tried to answer [this problem.] [My answer was] 3/4 [(=6/8)]. [My strategy was to] us[e] the union set operation [on] 4/8 [(=1/2)] and 3/8 [i.e. \(\displaystyle \dfrac{4}{8} \bigcup \dfrac{3}{8}\)], based on what is being asked in the problem.
 
Actually, I think there's only one answer in their post, although it was written quite poorly, and, frankly, it was kind of a mess. Here's what I interpreted it as saying:
I interpreted it as you have (when I answered the same question at another site) and cannot deny that it was not well worded. But I cut kids a bunch of slack when their questions involve incorrect answer keys or incorrect multiple choices: they have a right to be confused under those circumstances.
 
But I cut kids a bunch of slack when their questions involve incorrect answer keys or incorrect multiple choices: they have a right to be confused under those circumstances.
I guess you are correct.
 
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